Well, you can use a larger hook, an I or J. Look at the numbers for the different sizes; usually there's an even amount of stitch increments between them, something like 8 or 10. Just add to that, going up to the sizes you need. It's better to look at the actual measurements, rather than to figure you need to go 5 sizes up. A size 12 may not correspond to a dress or sweater size 12, but might actually be larger or smaller.

If you don't like the idea of using a larger hook (which will make this cardigan even more holey than it already is), you could instead add repeats of the pattern (usually found between the asterisks) until it is the right size.

The great thing about crochet is that you can easily measure it against yourself (or another cardigan that fits similar to how you want your creation to fit). Unlike knitting, which requires inserting a lifeline and removing your needles, crochet allows you to pull out your hook at any point and take measurements. The tricky part will be understanding (and translating to your size) how they do the decreases and increases while staying in pattern. If you read the sections about shaping carefully, you might be able to translate these exceptions to the pattern over to your size.

And you know, sites like that need to "get with it." How many women do you know that actually wear a size 12? Maybe 40 years ago. They're really shutting themselves out of the market by not catering to plus size women like us.

If the pattern bust is 38 inches, and you need 46 inches, do as Antares said and add extra motifs. It looks like the only shaping is at the neck, the sides seem to be straight up and down. See how many stitches it states for the 38 inch size, and figure out how many more you need for 8 more inches. Then work the pattern stitch (you may need to add a few extra stitches to make the repeats work put) straight up until you get to the neck shaping, which will not change.You will probably need to make the armhole openings longer, and the sleeves wider to match, but that will be done in the same way, by adding more stitches to the original directions.

It might also be helpful to make a gauge swatch in whatever st is recommended or in the pattern st in order to determine how many sts/inch you're getting with your hook and yarn. Then you can enlarge the pattern with that number in mind.